Pakistan · Class 12 · Practice Sheet 31

1. 1.

   Find the gravitational potential energy of a 43 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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3. 3.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 7 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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4. 4.

   An object with initial velocity 1 m/s accelerates at 2.5 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   Find the population standard deviation of: 13, 11, 7, 18, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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6. 6.

   In a triangle, a = 17, b = 12 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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7. 7.

   A device runs at 35 V drawing 9.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A population of 1,500 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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9. 9.

   A device runs at 208 V drawing 4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the momentum of a 34 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A force of 38 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    In a triangle, a = 11, b = 15 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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13. 13.

    Find the force needed to accelerate a 16 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the population standard deviation of: 19, 19, 16, 2, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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15. 15.

    A device runs at 57 V drawing 4.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    ₨2,100 is invested at 8% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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17. 17.

    A current of 6.8 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A force of 100 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A population of 2,100 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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20. 20.

    A force of 101 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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